Search results for: Mathematical Analysis courses.

Authors: E. Ramprasath, P. Manojkumar, P. Veena

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Proposed paper dealt with the modelling and analysis of induction motor based on the mathematical expression using the graphical programming environment of Laboratory Virtual Instrument Engineering Workbench (LabVIEW). Induction motor modelling with the mathematical expression enables the motor to be simulated with the various required parameters. Owing to the invention of variable speed drives study about the induction motor characteristics became complex. In this simulation motor internal parameter such as stator resistance and reactance, rotor resistance and reactance, phase voltage, frequency and losses will be given as input. By varying the speed of motor corresponding parameters can be obtained they are input power, output power, efficiency, torque induced, slip and current.

Keywords: Induction motor, LabVIEW software, modelling and analysis, electrical and mechanical characteristics of motor.

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Authors: M.R.Shabgard, R.M.Shotorbani

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FW4 is a newly developed hot die material widely used in Forging Dies manufacturing. The right selection of the machining conditions is one of the most important aspects to take into consideration in the Electrical Discharge Machining (EDM) of FW4. In this paper an attempt has been made to develop mathematical models for relating the Material Removal Rate (MRR), Tool Wear Ratio (TWR) and surface roughness (Ra) to machining parameters (current, pulse-on time and voltage). Furthermore, a study was carried out to analyze the effects of machining parameters in respect of listed technological characteristics. The results of analysis of variance (ANOVA) indicate that the proposed mathematical models, can adequately describe the performance within the limits of the factors being studied.

Keywords: Electrical Discharge Machining (EDM), linearregression technique, Response Surface Methodology (RSM)

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Authors: Troy L. Story

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Mathematical models of dynamics employing exterior calculus are mathematical representations of the same unifying principle; namely, the description of a dynamic system with a characteristic differential one-form on an odd-dimensional differentiable manifold leads, by analysis with exterior calculus, to a set of differential equations and a characteristic tangent vector (vortex vector) which define transformations of the system. Using this principle, a mathematical model for economic growth is constructed by proposing a characteristic differential one-form for economic growth dynamics (analogous to the action in Hamiltonian dynamics), then generating a pair of characteristic differential equations and solving these equations for the rate of economic growth as a function of labor and capital. By contracting the characteristic differential one-form with the vortex vector, the Lagrangian for economic growth dynamics is obtained.

Keywords: Differential geometry, exterior calculus, Hamiltonian geometry, mathematical economics.

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Authors: Stanislav Aryeh V. Fradkin, Sharif E.Guseynov

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There is a complex situation on the transport environment in the cities of the world. For the analysis and prevention of environmental problems an accurate calculation hazardous substances concentrations at each point of the investigated area is required. In the turbulent atmosphere of the city the wellknown methods of mathematical statistics for these tasks cannot be applied with a satisfactory level of accuracy. Therefore, to solve this class of problems apparatus of mathematical physics is more appropriate. In such models, because of the difficulty as a rule the influence of uneven land surface on streams of air masses in the turbulent atmosphere of the city are not taken into account. In this paper the influence of the surface roughness, which can be quite large, is mathematically shown. The analysis of this problem under certain conditions identified the possibility of areas appearing in the atmosphere with pressure tending to infinity, i.e. so-called "wall effect".

Keywords: Air pollution, concentration of harmful substances, physical-mathematical model, urban area.

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Authors: Nabil Sultan

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A great deal has been written on Massive Open Online Courses (MOOCs) since 2012 (considered by some as the year of the MOOCs). The emergence of MOOCs caused a great deal of interest amongst academics and technology experts as well as ordinary people. Some of the authors who wrote on MOOCs perceived it as the next big thing that will disrupt education. Other authors saw it as another fad that will go away once it ran its course (as most fads often do). But MOOCs did not turn out to be a fad and it is still around. Most importantly, they evolved into something that is beginning to look like a viable business model. This paper explores this phenomenon within the theoretical frameworks of disruptive innovations and jobs to be done as developed by Clayton Christensen and his colleagues and its implications for the future of higher education (HE).

Keywords: MOOCs, disruptive innovations, higher education, jobs theory.

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Authors: Muhammad Shahid, Nasir-uddin Khan, Mushtaq Hussain, Muhammad Liaquat Ali, Asif Mansoor

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Tuberculosis (TB) remains a leading cause of infectious mortality. It is primarily transmitted by the respiratory route, individuals with active disease may infect others through airborne particles which releases when they cough, talk, or sing and subsequently inhale by others. In order to study the effect of the Bacilli Calmette-Guerin (BCG) vaccine after vaccination of TB patient, a Vaccinated Susceptible Infected and Recovered (VSIR) mathematical model is being developed to achieve the desired objectives. The mathematical model, so developed, shall be used to quantify the effect of BCG Vaccine to protect the immigrant young adult person. Moreover, equations are to be established for the disease endemic and free equilibrium states and subsequently utilized in disease stability analysis. The stability analysis will give a complete picture of disease annihilation from the total population if the total removal rate from the infectious group should be greater than total number of dormant infections produced throughout infectious period.

Keywords: Bacillus Calmette-Guerin vaccine, disease-free equilibrium state, VSIR Quantification, disease stability analysis.

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Authors: Kamila Janovská, Šárka Vilamová, Petr Besta, Iveta Vozňáková, Roman Kozel

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Quantitative methods of economic decision-making as the methodological base of the so called operational research represent an important set of tools for managing complex economic systems,both at the microeconomic level and on the macroeconomic scale. Mathematical models of controlled and controlling processes allow, by means of artificial experiments, obtaining information foroptimalor optimum approaching managerial decision-making.The quantitative methods of economic decision-making usually include a methodology known as structural analysis -an analysisof interdisciplinary production-consumption relations.

Keywords: economic decision-making, mathematical methods, structuralanalysis, technical coefficient

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Authors: Kuan-Chou Chen, Keh-Wen “Carin” Chuang

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This paper demonstrates a model of an e-Learning system based on nowadays learning theory and distant education practice. The relationships in the model are designed to be simple and functional and do not necessarily represent any particular e- Learning environments. It is meant to be a generic e-Learning system model with implications for any distant education course instructional design. It allows online instructors to move away from the discrepancy between the courses and body of knowledge. The interrelationships of four primary sectors that are at the e-Learning system are presented in this paper. This integrated model includes [1] pedagogy, [2] technology, [3] teaching, and [4] learning. There are interactions within each of these sectors depicted by system loop map.

Keywords: e-Learning system, online courses instructionaldesign, integrated model, interrelationships.

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Authors: N. Khatiashvili, Ch. Pirumova, V. Akhobadze

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In the paper the mathematical model of tumor growth is considered. New capillary network formation, which supply cancer cells with the nutrients, is taken into the account. A formula estimating a tumor growth in connection with the number of capillaries is obtained.

Keywords: Differential Equations, Mathematical Models, Vascular Endothelial, Tumor

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Authors: Robert L. Burdett, Bayan Bevrani

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Analytical techniques for measuring and planning railway capacity expansion activities have been considered in this article. A preliminary mathematical framework involving track duplication and section sub divisions is proposed for this task. In railways, these features have a great effect on network performance and for this reason they have been considered. Additional motivations have also arisen from the limitations of prior models that have not included them.

Keywords: Capacity analysis, capacity expansion, railways.

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Authors: Thossaporn Thossansin, Auttapon Pomsathit

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This paper presents a comparison between using a desktop web application and a mobile application for students enrolling in courses at Rangsit University, Thailand. In addition, Rangsit University has enhanced the enrollment process by leveraging its information systems, which allows students to choose to enroll in courses online. In order to use the system, students must provide their identification and personal documents for registration. The reason to have a mobile application is to support students’ ability to access the system at anytime, anywhere and anyplace. The objective of this paper was to: 1. Evaluate the success of developing a user friendly mobile device system and 2. Measure user interest in future mobile development.

Keywords: Mobile Application, Web Application and Enrollment System.

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Authors: Jaroslav Krutil, František Pochylý, Simona Fialová

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The article presents two mathematical models of the interaction between a rotating shaft and an incompressible fluid. The mathematical model includes both the journal bearings and the axially traversed hydrodynamic sealing gaps of hydraulic machines. A method is shown for the identification of additional effects of the fluid acting on the rotor of the machine, both for a linear and a nonlinear model. The interaction is expressed by matrices of mass, stiffness and damping.

Keywords: CFD modeling, hydrodynamic gap, matrices of mass, stiffness and damping, nonlinear mathematical model.

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Authors: Norazlina Khamis, Sufian Idris, Rodina Ahmad

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The most influential programming paradigm today is object oriented (OO) programming and it is widely used in education and industry. Recognizing the importance of equipping students with OO knowledge and skills, it is not surprising that most Computer Science degree programs offer OO-related courses. How do we assess whether the students have acquired the right objectoriented skills after they have completed their OO courses? What are object oriented skills? Currently none of the current assessment techniques would be able to provide this answer. Traditional forms of OO programming assessment provide a ways for assigning numerical scores to determine letter grades. But this rarely reveals information about how students actually understand OO concept. It appears reasonable that a better understanding of how to define and assess OO skills is needed by developing a criterion referenced model. It is even critical in the context of Malaysia where there is currently a growing concern over the level of competency of Malaysian IT graduates in object oriented programming. This paper discussed the approach used to develop the criterion-referenced assessment model. The model can serve as a guideline when conducting OO programming assessment as mentioned. The proposed model is derived by using Goal Questions Metrics methodology, which helps formulate the metrics of interest. It concluded with a few suggestions for further study.

Keywords: Object-oriented programming, programmingassessment, criterion-referenced assessment model, goal questionsmetrics.

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Authors: Lun-Ping Hung, Nan-Chen Hsieh, Chia-Ling Ho, Chien-Liang Chen

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Currently, most of distance learning courses can only deliver standard material to students. Students receive course content passively which leads to the neglect of the goal of education – “to suit the teaching to the ability of students". Providing appropriate course content according to students- ability is the main goal of this paper. Except offering a series of conventional learning services, abundant information available, and instant message delivery, a complete online learning environment should be able to distinguish between students- ability and provide learning courses that best suit their ability. However, if a distance learning site contains well-designed course content and design but fails to provide adaptive courses, students will gradually loss their interests and confidence in learning and result in ineffective learning or discontinued learning. In this paper, an intelligent tutoring system is proposed and it consists of several modules working cooperatively in order to build an adaptive learning environment for distance education. The operation of the system is based on the result of Self-Organizing Map (SOM) to divide students into different groups according to their learning ability and learning interests and then provide them with suitable course content. Accordingly, the problem of information overload and internet traffic problem can be solved because the amount of traffic accessing the same content is reduced.

Keywords: Distance Learning, Intelligent Tutoring System(ITS), Self-Organizing Map (SOM)

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Authors: S. Chiali, Z.Eberrichi, M.Malki

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The number of framework conceived for e-learning constantly increase, unfortunately the creators of learning materials and educational institutions engaged in e-formation adopt a “proprietor" approach, where the developed products (courses, activities, exercises, etc.) can be exploited only in the framework where they were conceived, their uses in the other learning environments requires a greedy adaptation in terms of time and effort. Each one proposes courses whose organization, contents, modes of interaction and presentations are unique for all learners, unfortunately the latter are heterogeneous and are not interested by the same information, but only by services or documents adapted to their needs. Currently the new tendency for the framework conceived for e-learning, is the interoperability of learning materials, several standards exist (DCMI (Dublin Core Metadata Initiative)[2], LOM (Learning Objects Meta data)[1], SCORM (Shareable Content Object Reference Model)[6][7][8], ARIADNE (Alliance of Remote Instructional Authoring and Distribution Networks for Europe)[9], CANCORE (Canadian Core Learning Resource Metadata Application Profiles)[3]), they converge all to the idea of learning objects. They are also interested in the adaptation of the learning materials according to the learners- profile. This article proposes an approach for the composition of courses adapted to the various profiles (knowledge, preferences, objectives) of learners, based on two ontologies (domain to teach and educational) and the learning objects.

Keywords: Adaptive educational hypermedia systems (AEHS), E-learning, Learner's model, Learning objects, Metadata, Ontology.

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Authors: Juliana A. Knocikova, Yann Bouret, Médéric Argentina, Laurent Counillon

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Cell volume, together with membrane potential and intracellular hydrogen ion concentration, is an essential biophysical parameter for normal cellular activity. Cell volumes can be altered by osmotically active compounds and extracellular tonicity. In this study, a simple mathematical model of osmotically induced cell swelling and shrinking is presented. Emphasis is given to water diffusion across the membrane. The mathematical description of the cellular behavior consists in a system of coupled ordinary differential equations. We compare experimental data of cell volume alterations driven by differences in osmotic pressure with mathematical simulations under hypotonic and hypertonic conditions. Implications for a future model are also discussed.

Keywords: Eukaryotic cell, mathematical modeling, osmosis, volume alterations.

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Authors: Hao-Hsi Tseng, Hsin-Yun Lee, Yu-Cheng Kuo

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In order to understand whether there is a better than the learning function of learning methods and improve the CAD Courses for enterprise’s design human resource development, this research is applied in learning practical learning computer graphics software. In this study, Revit building information model for learning content, design of two different modes of learning curriculum to learning, learning functions, respectively, and project learning. Via a post-test, questionnaires and student interviews, etc., to study the effectiveness of a comparative analysis of two different modes of learning. Students participate in a period of three weeks after a total of nine-hour course, and finally written and hands-on test. In addition, fill in the questionnaire response by the student learning, a total of fifteen questionnaire title, problem type into the base operating software, application software and software-based concept features three directions. In addition to the questionnaire, and participants were invited to two different learning methods to conduct interviews to learn more about learning students the idea of two different modes. The study found that the ad hoc short-term courses in learning, better learning outcomes. On the other hand, functional style for the whole course students are more satisfied, and the ad hoc style student is difficult to accept the ad hoc style of learning.

Keywords: Development, education, human resource, learning.

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Authors: N. Hammid, F. Bouarab-Dahmani, T. Berkane

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Since its appearance, the MOOC (massive open online course) is gaining more and more intention of the educational communities over the world. Apart from the current MOOCs design and purposes, the creators of MOOC focused on the importance of the connection and knowledge exchange between individuals in learning. In this paper, we present a conceptual model for massive open online blended courses where teachers over the world can collaborate and exchange their experience to get a common efficient content designed as a MOOC opened to their students to live a better learning experience. This model is based on disciplines’ concepts capitalization and the detection of the obstacles met by their students when faced with problem situations (exercises, projects, case studies, etc.). This detection is possible by analyzing the frequently of semantic errors committed by the students. The participation of teachers in the design of the course and the attendance by their students can guarantee an efficient and extensive participation (an important number of participants) in the course, the learners’ motivation and the evaluation issues, in the way that the teachers designing the course assess their students. Thus, the teachers review, together with their knowledge, offer a better assessment and efficient connections to their students.

Keywords: MOOC, Massive Open Online Courses, Online learning, E-learning, Blended learning.

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Authors: Priyanka Gupta, Paul Verma, Kerry Hourigan, Jayesh Bellare, Sameer Jadhav

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Understanding the consumption and production of various metabolites of fibroblast conditioned media is needed for its proper and optimized use in expansion of pluripotent stem cells. For this purpose, we have used the HPLC method to analyse the consumption of glucose and the production of lactate over time by mouse embryonic fibroblasts. The experimental data have also been compared with mathematical model fits. 0.025 moles of lactate was produced after 72 hrs while the glucose concentration decreased from 0.017 moles to 0.011 moles. The mathematical model was able to predict the trends of glucose consumption and lactate production.

Keywords: Conditioned media, HPLC, metabolite analysis, mouse embryonic fibroblast.

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Authors: Carol Shepherd, Madelon Alpert, Marilyn Koeller

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In order to provide and maintain effective pedagogy for the burgeoning virtual reality community, it is vital to have trained faculty in the institutions of higher education who will teach these courses and be able to make full use of their academic knowledge and expertise. As the number of online courses continues to grow, there is a need for these institutions to establish mentoring programs that will support the novice online instructor. The environment in which this takes place and the factors that ensure its success are critical to the adoption of the new instructional delivery format taught by both seasoned educators and adjunct instructors. Effective one-on-one mentoring promotes a professional, compassionate and collegial faculty who will provide a consistent and rigorous academic program for students online.

Keywords: Mentoring seasoned faculty, staff development, online pedagogy, online andragogy.

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Authors: C. Rogerson, E. Scott

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The purpose of this paper is to consider the introduction of online courses to replace the current classroom-based staff training. The current training is practical, and must be completed before access to the financial computer system is authorized. The long term objective is to measure the efficacy, effectiveness and efficiency of the training, and to establish whether a transfer of knowledge back to the workplace has occurred. This paper begins with an overview explaining the importance of staff training in an evolving, competitive business environment and defines the problem facing this particular organization. A summary of the literature review is followed by a brief discussion of the research methodology and objective. The implementation of the alpha version of the online course is then described. This paper may be of interest to those seeking insights into, or new theory regarding, practical interventions of online learning in the real world.

Keywords: Computer-based courses, e-learning, online training, workplace training.

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Authors: Beata Jackowska-Zduniak

Abstract:

We formulate and analyze a mathematical model describing dynamics of the hypothalamus-pituitary-thyroid homoeostatic mechanism in endocrine system. We introduce to this system two types of couplings and delay. In our model, feedback controls the secretion of thyroid hormones and delay reflects time lags required for transportation of the hormones. The influence of delayed feedback on the stability behaviour of the system is discussed. Analytical results are illustrated by numerical examples of the model dynamics. This system of equations describes normal activity of the thyroid and also a couple of types of malfunctions (e.g. hyperthyroidism).

Keywords: Mathematical modeling, ordinary differential equations, endocrine system, stability analysis.

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Authors: Rujira Kongnuy, Puntani Pongsumpun, I-Ming Tang

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Dengue fever is an important human arboviral disease. Outbreaks are now reported quite often from many parts of the world. The number of cases involving pregnant women and infant cases are increasing every year. The illness is often severe and complications may occur. Deaths often occur because of the difficulties in early diagnosis and in the improper management of the diseases. Dengue antibodies from pregnant women are passed on to infants and this protects the infants from dengue infections. Antibodies from the mother are transferred to the fetus when it is still in the womb. In this study, we formulate a mathematical model to describe the transmission of this disease in pregnant women. The model is formulated by dividing the human population into pregnant women and non-pregnant human (men and non-pregnant women). Each class is subdivided into susceptible (S), infectious (I) and recovered (R) subclasses. We apply standard dynamical analysis to our model. Conditions for the local stability of the equilibrium points are given. The numerical simulations are shown. The bifurcation diagrams of our model are discussed. The control of this disease in pregnant women is discussed in terms of the threshold conditions.

Keywords: Dengue disease, local stability, mathematical model, pregnancy.

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Authors: C. Matasane, C. Dwarika, R. Naidoo

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The mathematical analysis on radiation obtained and the development of the solar photovoltaic (PV) array groundwater pumping is needed in the rural areas of Thohoyandou for sizing and power performance subject to the climate conditions within the area. A simple methodology approach is developed for the directed coupled solar, controller and submersible ground water pump system. The system consists of a PV array, pump controller and submerged pump, battery backup and charger controller. For this reason, the theoretical solar radiation is obtained for optimal predictions and system performance in order to achieve different design and operating parameters. Here the examination of the PV schematic module in a Direct Current (DC) application is used for obtainable maximum solar power energy for water pumping. In this paper, a simple efficient photovoltaic water pumping system is presented with its theoretical studies and mathematical modeling of photovoltaics (PV) system.

Keywords: Renewable energy sources, solar groundwater pumping, theoretical and mathematical analysis of photovoltaic (PV) system, theoretical solar radiation.

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Authors: Ibrahim S AlNomay, Alaa Jaber, Ghada AlNasser

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A learning management system (commonly abbreviated as LMS) is a software application for the administration, documentation, tracking, and reporting of training programs, classroom and online events, e-learning programs, and training content (Ellis 2009). (Hall 2003) defines an LMS as \"software that automates the administration of training events. All Learning Management Systems manage the log-in of registered users, manage course catalogs, record data from learners, and provide reports to management\". Evidence of the worldwide spread of e-learning in recent years is easy to obtain. In April 2003, no fewer than 66,000 fully online courses and 1,200 complete online programs were listed on the TeleCampus portal from TeleEducation (Paulsen 2003). In the report \" The US market in the Self-paced eLearning Products and Services:2010-2015 Forecast and Analysis\" The number of student taken classes exclusively online will be nearly equal (1% less) to the number taken classes exclusively in physical campuses. Number of student taken online course will increase from 1.37 million in 2010 to 3.86 million in 2015 in USA. In another report by The Sloan Consortium three-quarters of institutions report that the economic downturn has increased demand for online courses and programs.

Keywords: LMS, Interactive Materials, Exam Centers, Learning Outcomes

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Authors: S. Bennoud, M. Zergoug

Abstract:

The numerical simulation of electromagnetic interactions is still a challenging problem, especially in problems that result in fully three dimensional mathematical models.

The goal of this work is to use mathematical modeling to characterize the reliability and capacity of eddy current technique to detect and characterize defects embedded in aeronautical in-service pieces.

The finite element method is used for describing the eddy current technique in a mathematical model by the prediction of the eddy current interaction with defects. However, this model is an approximation of the full Maxwell equations.

In this study, the analysis of the problem is based on a three dimensional finite element model that computes directly the electromagnetic field distortions due to defects.

Keywords: Eddy current, Finite element method, Non destructive testing, Numerical simulations.

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Authors: Imelda Smit

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Systems Analysis and Design is a key subject in Information Technology courses, but students do not find it easy to cope with, since it is not “precise" like programming and not exact like Mathematics. It is a subject working with many concepts, modeling ideas into visual representations and then translating the pictures into a real life system. To complicate matters users who are not necessarily familiar with computers need to give their inputs to ensure that they get the system the need. Systems Analysis and Design also covers two fields, namely Analysis, focusing on the analysis of the existing system and Design, focusing on the design of the new system. To be able to test the analysis and design of a system, it is necessary to develop a system or at least a prototype of the system to test the validity of the analysis and design. The skills necessary in each aspect differs vastly. Project Management Skills, Database Knowledge and Object Oriented Principles are all necessary. In the context of a developing country where students enter tertiary education underprepared and the digital divide is alive and well, students need to be motivated to learn the necessary skills, get an opportunity to test it in a “live" but protected environment – within the framework of a university. The purpose of this article is to improve the learning experience in Systems Analysis and Design through reviewing the underlying teaching principles used, the teaching tools implemented, the observations made and the reflections that will influence future developments in Systems Analysis and Design. Action research principles allows the focus to be on a few problematic aspects during a particular semester.

Keywords: Action Research, Project Development, Systems Analysis and Design, Technology in Teaching.

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Authors: A. Meydanlioglu, F. Arikan

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In recent years, thanks to the development of information and communication technologies, the computer and internet have been used widely in higher education. Internet-based education is impacting traditional higher education as online components increasingly become integrated into face- to- face (FTF) courses. The goal of combined internet-based and traditional education is to take full advantage of the benefits of each platform in order to provide an educational opportunity that can promote student learning better than can either platform alone. Research results show that the use of hybrid learning is more effective than online or FTF models in higher education. Due to the potential benefits, an increasing number of institutions are interested in developing hybrid courses, programs, and degrees. Future research should evaluate the effectiveness of hybrid learning. This paper is designed to determine the impact of hybrid learning on higher education.

Keywords: E-learning, higher education, hybrid learning, online education.

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Authors: Masao Okabe

Abstract:

Nowadays, in Japan, variety of students get into a university and one of the main roles of introductory courses for freshmen is to make such students well prepared for subsequent intermediate courses. For that purpose, the flipped-mastery model is not enough because videos usually used in a flipped classroom is not adaptive and does not fit all freshmen with different academic performances. This paper proposes an ontology-navigated tutoring system called EduGraph. Using EduGraph, students can prepare for and review a class, in a more flexibly personalizable way than by videos. Structuralizing learning materials by its ontology, EduGraph also helps students integrate what they learn as knowledge, and makes learning materials sharable. EduGraph was used for an introductory course for freshmen. This application suggests that EduGraph is effective.

Keywords: Adaptive e-learning, flipped classroom, mastery learning, ontology.

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Authors: Fereshteh Afkari, Davood Bagheri

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The effect of teaching method on learning assistance Dunn Review .The study, to compare the effects of collaboration on teaching mathematics learning courses, including writing, science, experimental girl students by other methods of teaching basic first paid and the amount of learning students methods have been trained to cooperate with other students with other traditional methods have been trained to compare. The survey on 100 students in Tehran that using random sampling ¬ cluster of girl students between the first primary selections was performed. Considering the topic of semi-experimental research methods used to practice the necessary information by questionnaire, examination questions by the researcher, in collaboration with teachers and view authority in this field and related courses that teach these must have been collected. Research samples to test and control groups were divided. Experimental group and control group collaboration using traditional methods of mathematics courses, including writing and experimental sciences were trained. Research results using statistical methods T is obtained in two independent groups show that, through training assistance will lead to positive results and student learning in comparison with traditional methods, will increase also led to collaboration methods increase skills to solve math lesson practice, better understanding and increased skill level of students in practical lessons such as science and has been writing.

Keywords: method of teaching, learning, collaboration

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